In the US jurisprudence, the court is the determinator of law, the jury is the determinator of the facts.
Appeals can only be based on error of law, or suppression of facts (whether deliberate or unintentional. An unintentional suppression example is DNA evidence used to overturn wrongful convictions. The technology didn't exist at the time of conviction.). This may or may not require a retrial.
Jury findings are not appealable (unless deliberate malfeasance is proven). Jury finding in opposition of law are know to occur often. It's nicknamed (in Texas) as Jury Nullification...